Based on these observations, the investigators hypothesize that pharmacologic inhibition of matrix metalloproteinases by doxycycline will favorably modify the natural history of chronic obstructive pulmonary disease in HIV-infected patients. To test this hypothesis, the investigators propose conducting a proof of concept pilot study as a prelude to a possible phase II randomized, placebo-controlled trial (testing safety and efficacy in a larger population controlled with a "sugar pill") of doxycycline for COPD in HIV-infected patients should the proof of concept be successful. Our research team is lead by a pulmonologist/researcher with expertise in HIV-associated COPD and an infectious diseases specialist/clinical trials expert.